New Advancements in Pure and Applied Mathematics via Fractals and Fractional Calculus

• Format: eBook
• Language: English
• Published: Basel 2022
• Subjects: Mathematics and Science; Research and information: general; AB-fractional operator; Adomian decomposition method; asymptotic stability; Atangana-Baleanu fractional derivative operator; basin of attraction; bessel function; beta function; boundedness; Caputo derivative; Caputo fractional derivative; Caputo-Fabrizio derivative; Caputo-Hadamard fractional derivative; Caputo-Hadamard fractional integral; Cattaneo equation; computational cost; computational order of convergence; convex; cubic B-splines; delta function; efficiency index; Elzaki transform; Euler's integral of gamma functions; exponential convex; extended cubic B-splines; extremal solutions; Fejér-Hadamard inequality; Fisher's equation; fixed point theory; Fornberg-Whitham equation; Fox-Wright-function; fractal dimensions; fractional; fractional calculus; fractional div-curl systems; fractional kinetic equation; fractional transforms; fractional vector operators; fractional-order differential equations; generalized fractional kinetic equation; generalized hypergeometric series; Gould-Hopper-Laguerre-Sheffer matrix polynomials; Hadamard inequality; Halley's method; harmonically convex function; Helmholtz decomposition theorem; Hermite-Hadamard-type inequalities; Hilfer fractional derivative; Hölder's inequality; Hukuhara difference; hybrid Caputo-Hadamard fractional differential equation and inclusion; hybrid control; inequalities; Mittag-Leffler kernel; model calibration; monotone iterative method; n/a; Neimark-Sacker bifurcation; new iterative transform method; non-singular function involving kernel fractional operator; nonlinear models; operational matrices; operational methods; period-doubling bifurcation; prey-predator model; quantum; quasi-monomiality; Riemann zeta-function; Riemann-Liouville derivative; sequences; shifted Vieta-Lucas polynomials; system of Whitham-Broer-Kaup equations; thermostat modeling; trigonometric cubic B-splines; typhoid fever disease; umbral calculus; vaccination; weighted (k,s) fractional derivative; weighted (k,s) fractional integral operator; weighted generalized Laplace transform; Yang transform; ϑ-Caputo derivative
• Online Access: Open Access: DOAB: description of the publication; Open Access: DOAB, download the publication

 This reprint focuses on exploring new developments in both pure and applied mathematics as a result of fractional behaviour. It covers the range of ongoing activities in the context of fractional calculus by offering alternate viewpoints, workable solutions, new derivatives, and methods to solve real-world problems. It is impossible to deny that fractional behaviour exists in nature. Any phenomenon that has a pulse, rhythm, or pattern appears to be a fractal. The 17 papers that were published and are part of this volume provide credence to that claim. A variety of topics illustrate the use of fractional calculus in a range of disciplines and offer sufficient coverage to pique every reader's attention.